Proper conformal symmetries in SD Einstein spaces
General Relativity and Quantum Cosmology
2014-10-29 v1
Abstract
Proper conformal symmetries in self-dual (SD) Einstein spaces are considered. It is shown, that such symmetries are admitted only by the Einstein spaces of the type [N]x[N]. Spaces of the type [N]x[-] are considered in details. Existence of the proper conformal Killing vector implies existence of the isometric, covariantly constant and null Killing vector. It is shown, that there are two classes of [N]x[-]-metrics admitting proper conformal symmetry. They can be distinguished by analysis of the associated anti-self-dual (ASD) null strings. Both classes are analyzed in details. The problem is reduced to single linear PDE. Some general and special solutions of this PDE are presented.
Keywords
Cite
@article{arxiv.1403.1725,
title = {Proper conformal symmetries in SD Einstein spaces},
author = {Adam Chudecki and Michal Dobrski},
journal= {arXiv preprint arXiv:1403.1725},
year = {2014}
}